Theorems · Theorem · commutative algebra
IsLocalization.height_under
∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) {A : Type u_2} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[IsLocalization S A] (J : Ideal A), (Ideal.under R J).height = J.height- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.imageproof · cited by 5,609
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- iInfproof · cited by 1,690
- Ideal.IsPrimeproof · cited by 827
- IsLocalizationstatement and proof · cited by 636
- Ideal.comapproof · cited by 443
- iInf_congr_Propproof · cited by 218
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- IsLocalization.AtPrime.ringKrullDim_eq_heightproof · cited by 4
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimesproof · cited by 4
- UniqueFactorizationMonoid.iff_of_isLocalizationAway_of_primeproof · cited by 1
- IsLocalization.height_comapproof · cited by 0